Determining sample size for specification limits verification with tolerance intervals

In the traditional industrial verification process, when the aim is the compliance to assigned specifications, it is difficult to find an affordable statistical method for the purpose. Most data tables in industrial procedures and standards deal with tolerance limits neglecting the potential needs to verify assigned specification limits. A two-sided tolerance interval, combined with a bivariate statistical hypothesis test can be used to address this problem. The proposed risk-based approach leads to the determination of the minimum sample size with preestablished probabilities of Type I and Type II errors, that are essential elements for estimating the safety and reliability risk. A novel method is proposed for determination of the tolerance interval testing factors. This approach calculates the testing factors based on the deviation of the mean and the variance from the null hypothesis when a specified value of Type II error is found. The deviations of the mean and variance are determined in such a way that an assigned proportion of the population falls within the specification limits. Additional studies are provided to assess the robustness of the method for nonnormal environments and to compare it with other methods.